Conversion factors
Kurt Foster
All right, already! If you want a conversion factor, you might be able
to find it here. If not, you might be able to find it in one of the
references mentioned. I've posted this before, but what with all the
endless wrangling about pounds, newtons, kilograms etc, I guess it's time
to post it again...
HOW MUCH IS...
Following is a miscellany of units, currently or previously in everyday
use. They are derived from several sources. This version differs from
earlier ones chiefly in having more material on plane and solid angles, and
a new section about units of radioactivity.
The "Sourcebook on Atomic Energy", though 40 years old, is a good
reference for the history of the fundamental discoveries about radioactivity
and atomic energy; similarly for "Physics of the Atom".
The "CRC Handbook of Chemistry and Physics" is an excellent reference for
a wide variety of data on chemical elements and compounds; physical
properties; and up-to-date exposure limits for radioactive elements.
The "Handbook of Mathematical Functions" by Abramowitz and Stegun (Dover,
ISBN 0-486-61272-4) has a number of fundamental physical constants, other
basic units and conversion factors, but is an older reference. It uses the
previous definition of the meter in terms of light of a specific frequency
from Krypton-86. This definition was superseded in 1983 by the definition
of the meter given below.
The "Information Please Almanac" gives up-to-date information on a variety
of weights and measures. There are also more specialized references for
physics and chemistry; perhaps readers of this group could post or E-mail to
me the bibliographic information on these, for incorporation in possible
future renditions of this posting.
Thermodynamic and electrical units and standards are not detailed in this
posting. They can be found in the above-named references. In particular,
"Handbook of Mathematical Functions" explains the relations between the SI,
EMU and ESU electric and magnetic units. Webster's Second International
Dictionary has an extensive table of units used in many different countries,
running nearly 4 pages in a "full size" dictionary!
We express scientific notation "m.mmmmExxx" for "m.mmmm x 10^xxx".
--------------------------------------------------------------------------
1 second is the duration of
9,192,631,770 cycles of the hyperfine transition frequency of Cesium-133
--------------------------------------------------------------------------
The Meter is defined by the condition that light travels in vacuum at
299,792,458 meters per second.
--------------------------------------------------------------------------
The Kilogram is the mass of a lump of Platinum-Iridium alloy at the
International Bureau of Weights and Measures in Paris. The U.S. Bureau of
Standards has a duplicate kilogram mass. The mass of 1000 cubic centimeters
of liquid water at 1 Atmosphere pressure and 4 deg C, is nearly 1 kilogram.
******************************ENUMERATION*********************************
1 half-dozen = 6
1 dozen = 12
1 "baker's dozen" = 13
1 score = 20
1 gross = 12 dozen = 144
1 great gross = 12 gross = 1728
Avogadro's number = # elem particles in 1 mole = 6.022 E23 (approx)
Eddington's Number = 136 x 2^256; Sir Arthur Eddington wrote that there were
that many protons in the Universe, and an equal number
of electrons. (1.5747724 E79, approx)
For counting sheets of paper, the following are used:
1 quire = (formerly) 24 or (more recently) 25 sheets
1 ream = 20 quires = (formerly) 480 sheets or (more recently) 500 sheets
1 bundle = 2 reams (formerly) 960 sheets or (more recently) 1000 sheets
---------------------------------------------------------------------------
Some power-of-ten multipliers are denoted by standard prefixes (for words)
and suffixes (showing up after a numerical amount, before the abbreviation
of a unit), like "2 mg" for "2 milligrams".
STANDARD NUMERICAL PREFIXES AND SUFFIXES FOR POWER-OF-TEN MULTIPLIERS
yocto- y E-24
zepto- z E-21
atto- a E-18
femto- f E-15
pico- p E-12
nano- n E-9
micro- mu* E-6 *small Greek letter
milli- m E-3
centi- c E-2
deci- d E-1
deka- da 10
hect(o)- h E2
kilo- k E3
mega- M E6
giga- G E9
tera- T E12
peta- P E15
exa- E E18
zetta- Z E21
yotta- Y E24
In computer-related reference, sometimes "kilo-" or "K" is used to denote
multiplication by 1024 or 2^10; while "mega" or "M" is used for 1,048,576 or
2^20, and "giga" or "G" is used for 1,073,741,824 or 2^30.
************************CIRCULAR (ANGLE) MEASURE**************************
The radian measure of a plane angle is defined as follows. For any circle
having its center at the vertex of the angle, the ratio s/r of the arc
length s cut off by the angle, to the radius r of the circle, is always the
same. This number is the radian measure of the angle. The definition
extends in a straightforward manner to angles consisting of more than one
complete revolution. Also, when the direction of traversing the angle is
important (as with physics-related applications), the counterclockwise
direction is taken as positive, and clockwise as negative.
1 radian is a circular arc equal in length to the radius of the circle.
1 circle = 2*pi radians = 360 degrees
1 degree of arc = 1/360 circle = 1.7453292 E-2 radian
1 minute of arc = 1/60 degree = (approx) 2.908882 E-4 radian
1 second of arc = 1/60 minute = (approx) 4.848137 E-6 radian
1 "sign" = 30 degrees = 1/12 of a circle
1 right angle = 90 degrees = 1/4 circle = pi/2 radians
1 grad = 1/400 of a circle; a right angle is 100 grads
For objects of small apparent size, radian measure provides a convenient
relation between actual size and distance, and apparent size: if the actual
size (diameter, say) is s, and the distance is d, then the angular size is
approximately s/d radians.
Note: The formulas for length of a circular arc, or the area of a circular
sector, are simplest when the defining angle is measured in radians. Also,
the calculus formulas for derivatives of trig functions; the "small angle
approximations" for sine and tangent; and the usual power series for sine
and cosine -- these all are based on the angles being measured in RADIANS.
SOLID ANGLES IN 3-SPACE
"Solid" angles may also be defined in 3-space (roughly) as follows: Let C
be a simple closed curve in a plane, and P a point that is not in the plane.
The region enclosed by the rays emanating from P (the vertex) and passing
through C is then a solid angle. It's a generalization of the region inside
a right circular cone.
The steradian (stellar radian) measure of a solid angle is defined in a
manner analogous to the radian for plane angles: For any sphere centered
at the vertex, the ratio A/(r^2) of the included surface area A on the
sphere to the square of the sphere's radius r is always the same. This
ratio is the steradian measure of the solid angle. The steradian measure
of a whole sphere is 4*pi.
If the rays defining a solid angle are continued into full lines, the
two "nappes" of the "cone" obviously define solid angles of equal
steradian measure. This is equivalent to the fact that, for a hollow
spherical shell serving as a uniform source of an inverse-square force,
the force emanating from that shell cancels out completely within its
interior.
*********************************LENGTH***********************************
GENERAL
1 inch (in) = 0.0254 meter or 2.54 centimeters (cm) (exact by definition)
1 foot (ft) = 12 inches = 0.3048 meter
1 yard (yd) = 3 feet = 36 inches = 0.9144 meter
1 kilometer (km) = 1000 meters
1 statute mile (mi) = 5280 ft = 1760 yd = 1.609344 km
1 International Nautical Mile = 1.852 km (exact by def) or 1.151 mi
Note: The geographic, or nautical mile, was originally intended to be one
minute of arc (1/21600 part, or 1/60 of a degree) of a "great circle" on
the Earth's surface. The fact that the Earth isn't a perfect sphere, gave
rise to several different values. The above value, originally used by
France, has been adopted for international use. See "miscellaneous units"
for other values.
--------------------------------------------------------------------------
SURVEYORS' CHAIN MEASURE
1 link (li) = 7.92 inches
1 rod (rd) = 5 & 1/2 yards = 16 & 1/2 feet [also called perch or pole]
1 chain (ch) = 4 rd = 22 yd = 66 ft = 100 links (Gunter's chain)
80 chains, or 320 rods, make 1 statute mile (mi) or 5280 ft.
--------------------------------------------------------------------------
CLOTH MEASURE
1 nail (na) = 2.25 in
1 quarter (qr) = 4 na = 9 in = 1/4 yd
1 Ell Flemish (E. Fl.) = 3 qr = 27 in
1 yd = 4 qr = 36 in
1 Ell English (E. En.) = 5 qr = 1 & 1/4 yd = 45 in
1 Ell French (E. Fr.) = 6 qr = 1 & 1/2 yd = 4 & 1/2 ft = 54 in
1 bolt = 40 yards
--------------------------------------------------------------------------
TYPESETTING
1 point = 1/72 in, approx
Agate = (formerly) 5 & 1/2 point, now 1/14 in
Pica = 12 points = 1/6 in, approx
--------------------------------------------------------------------------
MISCELLANEOUS LENGTHS
1 fermi = E-15 m = 1 femtometer (fm)
1 Angstrom = E-10 meter
1 micron = E-6 meter
1 hand = 4 in.
1 span = 9 in.
1 cubit = 18 in.
1 sacred cubit = 22 in. [approx]
1 fathom = 6 feet
1 cable's length = (variously) 100 fathoms; 120 fathoms (US Navy);
608 ft (U.S.); 607.61 ft (Brit.)
1 furlong = 1/8 mi = 40 rd = 220 yd = 660 ft
1 U.S. Nautical Mile = 6080 ft = 10 U.S. cable's lengths
1 British Nautical Mile = 6076.6097 feet = 10 British cable's lengths
1 league = 3 statute miles
1 Astronomical Unit (AU) = 1.496 E11 m (avg Earth-Sun distance)
1 light-year = dist light travels in 1 yr = 9.46 E15 m (9.46 Pm) [approx]
1 parsec (parallax-second) = 3.26 light-years = 3.08 E16 m
**********************************TIME************************************
1 minute (min) = 60 seconds
1 hour (hr) = 60 min = 3600 sec
1 (solar) day = 24 hours = 1.44 E3 min = 8.64 E4 sec
1 week = 7 days = 168 hr = 1.008 E3 min = 6.048 E5 sec
1 fortnight = 2 weeks or 14 days
1 lunation = 29.5 days (approx)
1 (civil or calendar) year = 365 days
1 bissextile or leap year = 366 days
1 solar year = 365 days, 5 hours, 48 minutes, 45.5 sec (approx)
= 3.15569 E7 sec, approx
1 (common) lunar year = 12 lunar months = 354 days
**********************************AREA************************************
Note: An area of k "units square" means a square, k units on a side,
and contains k^2 square units.
1 barn = E-28 m^2 = E-24 cm^2 = 100 square fermis
1 are (a) = 100 square meters (m^2)
1 hectare = 100 ares = 10,000 m^2
1 square foot (sq ft or ft^2) = 144 square inches (sq in or in^2)
1 square yard (sq yd) = 9 square feet = 1296 in^2
1 Square = 100 square feet (used in building)
1 square rod (sq rd) = 30.25 sq yd or 272.25 sq ft
1 square chain = 16 sq rd = 4356 sq ft
1 acre = 160 sq rd = 10 square chains = 43560 sq ft
1 square mile (sq mi or mi^2) = 640 acres
1 section = 1 mile square
1 township = 6 miles square = 36 square miles, approx.
[In the U.S., a "township" is a land area enclosed by lines of latitude and
longitude, whose southern, eastern and western borders are each 6 miles
long.]
Note: 1 acre is 0.4047 hectare, approx; a hectare is 2.471 acres, approx
*****************************CUBIC CAPACITY*******************************
1 liter = 1000 cubic centimeters (cc); thus 1 cc = 1 milliliter (ml)
1 stere (S) = 1 cubic meter (m^3) = 1000 liters
1 dry pint = (dry pt) = 33.6003 in^3
1 dry quart (dry qt) = 67.2006 in^3
1 peck (pk) = 8 dry qt = 16 dry pt = 537.6048 in^3
1 bushel (bu) = 4 pk = 32 dry qt = 2150.42 in^3
1 heaped bushel = 1.278 bu = 2747.715 in^3
[Note: The bushel is (traditionally) the capacity of a circular cylinder
which is 18 & 1/2 inches in diameter, and 8 inches in height. It is the
standard for U.S. dry measure.]
1 (U.S.) fluid ounce (fl oz) = 1.8046875 cubic inches (in^3)
1 (U.S.) fluid (liquid) pint (fl pt)= 16 fl oz = 28.875 in^3
1 (U.S.) fluid (liquid) quart (fl qt) = 2 fl pt = 57.75 in^3
1 (U.S.) gallon (gal) = 4 fl qt = 8 fl pt = 128 fl oz = 231 in^3
[Note: the gallon of 231 in^3 is the U.S. standard liquid measure.]
1 British or Imperial quart = 69.354 in^3 = 1.201 U.S. fl qt
1 British or Imperial gallon = 277.42 in^3 = 1.201 U.S. gal
[Note: A British or Imperial pint would be half an Imperial quart, so 1.201
U.S. fl pt, or about 19.2 fl oz. However, the British or Imperial fluid
ounce is defined so that a British or Imperial gallon is 160 British or
Imperial fluid ounces, as opposed to 128 U.S. fluid ounces in a U.S.
gallon. Thus a British or Imperial pint would be 20 British or Imperial
fluid ounces.]
--------------------------------------------------------------------------
APOTHECARIES' FLUID MEASURE:
The Apothecaries' fluid ounce, pint, quart and gallon are the same as for
U.S. liquid measure. However, the fluid ounce is subdivided as follows:
1 fluid dram = 60 minims = 1/8 fl oz
1 fl oz = 8 fl drs = 480 minims
Thus 1 fl pt = 128 fl drs and 1 gal = 1024 fl drs.
--------------------------------------------------------------------------
WINE OR LIQUID MEASURE -- used for all liquids except beer, ale and
(formerly) milk.
The ounce, pint, quart and gallon are the same as for U.S. liquid measure.
1 gill = 4 oz; 1 pt = 4 gills (gi)
1 barrel (bl) = 31 & 1/2 gal
1 tierce (tr) = 42 gal
1 hogshead (hhd) = 2 bl = 63 gal
1 puncheon (pn) = 2 tr = 84 gal
1 pipe (p) = 2 hhd = 3 tr = 4 bl = 126 gal
1 tun (T) = 4 hhd = 8 bl = 252 gal [sometimes a tun is larger.]
--------------------------------------------------------------------------
ALE OR BEER MEASURE -- for beer and ale (and formerly milk also).
The BEER GALLON is 282 in^3, not the U.S. standard 231 in^3 gallon! It is
divided into 4 quarts, and the quart into 2 pints.
1 beer pint = 35.25 in^3
1 beer quart = 2 beer pints = 70.5 in^3
1 barrel = 36 beer gallons
1 hogshead = 54 beer gallons
--------------------------------------------------------------------------
TIMBER AND LUMBER:
1 Board Foot (fbm) = 144 in^3 (12 in x 12 in by 1 in)
1 cord = 128 cu ft (a stack of wood 8 ft long, 4 ft wide and 4 ft
high.)
1 cord foot = 16 cu ft = 1/8 of a cord stack of wood, along the 8 ft side;
thus, 1 cord = 8 cord feet.
1 tun = 40 cu ft round timber or 50 cu ft hewn timber.
--------------------------------------------------------------------------
MISCELLANEOUS CUBIC MEASURES
1 teaspoon (tsp) = 1/6 fl oz, 5 ml approx
1 Tablespoon (Tbs) = 1/2 fl oz = 3 tsp = 15 ml, approx
1 Cup (C) = 1/2 fl pt = 8 fl oz = 240 ml, approx
1 fifth = 1/5 gal = 46.2 in^3 [usually for distilled liquor]
1 Magnum = a 2-quart bottle of wine or champagne
Molar volume of an ideal gas at STP = 22.414 liters
1 chaldron = 36 bu (Brit, some U.S. states) [used to measure coal]
1 chaldron = 32 bu (some U.S. states) [used to measure coal]
1 acre-foot = 43560 cu ft (a volume of water 1 ft deep, covering 1 acre.)
Note: 1 cu ft = 1728 in^3 is 7.4805 U.S. liquid gallons, approx. Thus,
an acre-foot of water is 325851.42 gallons, approximately. A water ration
of an acre-foot per year is approximately 892.74 gallons per day.
The term "barrel" is used variously to mean 105 dry quarts of dry goods
other than cranberries, but 86 & 45/64 dry quarts of cranberries; and there
quite a few "barrels" used in liquid measure, in addition to those given
above. SEE the "Information Please Almanac" for more details.
*****************************WEIGHT AND MASS******************************
Strictly speaking, a weight is a force -- the force exerted on a mass by
gravity. The weight of a mass m is W = mg, where g is the "acceleration of
gravity". Since this varies from place to place, even on Earth's surface,
"the" weight of a given mass isn't specified unless a "standard" gravity is
agreed on. The value for the "standard gravity" g_0 given in "Handbook of
Mathematical Functions" is 9.80665 m/sec^2. This is equivalent to 32.174048
ft/sec^2.
The kilogram is a mass unit. The force unit in the MKS (meter kilogram
second) system is the newton, 1 kg-m/sec^2; accordingly, a kilogram mass has
a weight of about 9.8 newtons in the MKS system (at least here on Earth). A
kilogram mass would only weigh 1.63 newtons on the Moon, however. In the
cgs (centimeter gram second) system, the mass unit is the gram (1 kg = 1000
g) and the force unit is the dyne, 1 g-cm/sec^2. Here on Earth, 1 qram
weighs about 980 dynes. Thus, 1 milligram (mg) weighs about 0.98 dyne here
on Earth.
Fortunately, there is no real harm in expressing "weights" in mass units,
PROVIDED this is understood to mean "has the same weight as". Thus, to say
something "weighs" 1 kilogram is technically incorrect, but, if understood
to mean "has the same weight as a kilogram mass", it would not only be
acceptable, but would remain true independent of location!
Note also that, if you "weigh" something in a balance, you are actually
comparing its mass to standard masses, and would get the same result,
regardless of location -- provided the gravitational field did not vary
appreciably over the balance! If, however, you use a spring scales for
weighing, you are then measuring the force exerted by gravity, and the
result WILL depend on location!
In the "English" or "British" system used in the U.S., UNFORTUNATELY, the
term "pound" is used to denote BOTH a mass AND a force. Not only that, but
there is a force unit related to the pound mass as the newton is to the
kilogram (1 poundal = 1 pound-ft/sec^2, "pound" = pound mass), as well as a
MASS unit related to the pound FORCE, as the kilogram is to the newton!
This mass is called the "slug", and the "pound force" is 1 slug-ft/sec^2.
A pound mass weighs about a pound force, also about 32 poundals, and a
slug mass weighs about 32 pounds force (on Earth). The pound force is used
in expressing pressure in "pounds per square inch" -- pressure has
"dimensionality" of force per area.
The "pounds" used in weighing are below taken as masses. The pound
Avoirdupois is defined as a mass, in terms of the kilogram. This furnishes
a definition of the "grain" as a mass. The other "English" units are given
in terms of MKS or cgs units for the sake of definiteness.
--------------------------------------------------------------------------
1 slug = 14.5939 kilogram (kg)
1 pound Avoirdupois (lb avdp) (mass) = 0.45359237 kg (exact)
1 dyne = 1 g-cm/sec^2
1 newton = 1 kg-m/sec^2 = E5 dynes
1 pound force = 4.44822 newtons
1 poundal = 0.138255 newton
--------------------------------------------------------------------------
AVOIRDUPOIS WEIGHT
1 grain (gr) = 64.79891 mg = 6.479891 E-5 kg exactly
1 dram (dr) = 27.34375 gr = 1.77184519525 g
1 ounce Avoirdupois (oz avdp) = 437.5 gr = 28.349523125 g = 16 dr
1 pound Avoirdupois (lb avdp) = 16 oz avdp = 256 dr = 453.59237 g = 7000 gr
1 quarter (qr) = 25 lb avdp
1 hundredweight ("short" or "net" hundred) (cwt) = 4 qr = 100 lb avdp
1 ton ("short" or "net" ton) = 20 cwt = 2000 lb avdp
--------------------------------------------------------------------------
TROY OR MINT WEIGHT -- for weighing precious metals
1 grain = 6.479891 E-5 kg = 64.79891 mg (exactly) [same as for avdp]
1 pennyweight (pwt) = 24 gr = 1.55517384 g
1 ounce Troy (oz) = 20 pwt = 480 gr = 31.1034768 g
1 pound Troy (lb) = 12 oz Troy = 240 pwt = 5760 gr = 373.2417216 g
--------------------------------------------------------------------------
APOTHECARIES' WEIGHT - for medicines
1 grain = 6.479891 E-5 kg = 64.79891 mg (exactly) [same as for avdp]
1 scruple = 20 gr = 1.2959782 g
1 dram = 3 scruples = 60 gr = 3.8879346 g
1 ounce = 8 drams = 480 gr = 31.1034768 g
1 pound = 12 ounces = 5760 gr = 373.2417216 g
Note: the symbols for the apothecaries' scruple, dram and ounce can't be
rendered easily in ASCII. The ounce and pound are the same in Troy and
Apothecaries' weight, but the ounce is subdivided differently.
--------------------------------------------------------------------------
MISCELLANEOUS WEIGHTS
1 carat = 200 mg -- used for weighing precious stones
Note: Older versions of the carat may vary somewhat.
1 assay ton = 29.167 g
Note: The number of milligrams of precious metal in an assay ton of ore,
equals the number of Troy ounces of precious metal in a ton (2000 lb avdp)
of the same ore.
1 quintal = 100 kg
Note: sometimes, a "quintal" means 100 lb avdp of fish
1 metric ton or "tonneau" = 1000 kg
1 "stone" = 14 lb avdp
1 "long quarter" = 28 lb avdp
1 "long hundred" = 112 lb avdp
1 "long ton" = 2240 lb avdp
The term "barrel" has been used for 196 lb avdp of flour, and 200 lb avdp
of beef or pork, as well as a plethora of different cubic capacities.
The term "bale" is used generically to mean a large bundle of goods. A
bale of cotton in the U.S. weighs about 500 lb avdp.
The term "quarter" was once used in England for selling wheat. It
consisted of 8 bushels, each weighing 70 lb avdp.
Note: 1 liter of liquid water at 1 Atmosphere pressure and 4 deg C, has a
mass of very nearly 1 kg; 1 cc thus has a mass very nearly equal to 1 gram.
******************************RADIOACTIVITY********************************
The methods used to assess the health hazards of radioactive elements and
compounds, and the corresponding units, are now legion. The aim of this
work is merely to give the basic framework, and units used to describe
radioactivity, so the reader may more easily follow discussions of the
topic.
The detailed consideration of the health hazards of radioactive materials,
and methods to control the risks, is the province of "Health Physics".
The first observation that Uranium compounds emitted penetrating rays
(without previous exposure to sunlight) was by Henri Becquerel in 1896. The
principal emissions (alpha, beta and gamma rays) were all discovered and
unambiguously characterized by 1914. Alpha particles (rays) are helium
nuclei, consisting of 2 protons and 2 neutrons. Beta particles are high
speed electrons. Gamma rays are (usually very energetic) electromagnetic
radiation. Becquerel shared the 1903 Nobel Prize in Physics with Pierre and
Marie Curie (he for his work on spontaneous radioactivity, the Curies for
their studies of radiation).
The term "radioactive" seems to have been coined by Marie Curie to
describe the emission of ionizing radiation by some elements. It first
appeared in print in 1898, in a paper by Marie and Pierre Curie entitled "On
a new radioactive substance contained in pitchblende" which concluded as
follows:
"If the existence of this new metal is confirmed, we propose to call it
*polonium*, after the name of the native country of one of us [Madame
Curie]."
The discovery was confirmed, and Marie Curie won the 1911 Nobel Prize in
Chemistry for the discovery of the elements Polonium and Radium. She thus
became the first (and so far only) person ever to win Nobel Prizes in two
different areas (she shared the 1903 Nobel Prize in Physics [see above]).
The theory of radioactive decay was proposed in 1902 by Ernest Rutherford
and Frederick Soddy. (Rutherford won the 1908 Nobel Prize in Chemistry for
his investigations of nuclear disintegration of elements.) For a given
radionuclide, there is a positive constant k such that the rate of decay
dN/dt (atoms per unit time) is given by
dN/dt = -k * N
where N is the number of atoms present and t is time. The minus sign
denotes the fact that N is decreasing with time. If N(0) is the number of
atoms initially present (ie at time 0) then the number N(t) present at time
t is given by
N(t) = N(0) * exp(-k*t)
where exp() is the exponential to the base "e". The constant k (called
the radioactive constant or decay constant, and sometimes denoted by a small
lambda) has units of 1/time (eg "per second"). The reciprocal 1/k is the
"average" life; this is the average time before decay of an atom in the
sample, in the sense of mathematical expectation. But probably the
best-known figure is the "half-life", which is ln(2)/k, or .69315/k,
approximately; ln() is the "natural" log; that is, log to the base "e".
Plugging the half-life H in for "t" in the above equation gives N(H) = N(0)
* (1/2), so the half-life is the time required for half the atoms initially
present to decay. After two half-lives, only 1/4 of the initial amount
remains; after three half-lives, only 1/8 remains, and so on. Note that the
decay constant k may also be obtained from the half-life H via k = ln(2)/H =
.69315/H, approximately. It may be necessary to convert the time unit, eg
from years to seconds, in order to get k in "per second" units.
One unit of radioactivity based directly on the rate of decay is the
curie,
1 curie (1 ci) = 3.7 E10 atomic disintegrations/sec.
The curie was originally intended to reflect the radioactivity of 1g of
radium (Ra-226). However, early values of its half-life were not very
precise, and successive refinements caused the value of the curie to keep
changing. The above value was taken, once and for all, for the sake of
definiteness. [Actually, 1g of Ra-226 undergoes about 3.61 E10
disintegrations per sec] One then defines a curie of a radioactive
substance as the amount whose rate of decay is 3.7 E10 atoms per
second. The nearness of the curie to the radioactivity of 1g of Ra-226
gives a convenient formula to estimate the mass M of 1 curie of any
substance, if its atomic (or molecular) weight W and half-life H (yr)
are known:
M = (H/1620 yr) * (W/226) grams, approx
and this could be refined by multiplying by 1.025. For example, the
half-life of U-238 is 4.5 E9 yr (and its atomic weight is 238). So one
curie of U-238 is M = (4.5E9/1.62E3)(238/226) = 2.925 E6 g approx, or
1.025 * 2.925 E6 = 2.998 E6 g more nearly -- nearly 3 metric tons!
Because the curie is a large unit, the microcurie is more commonly used; a
microcurie of U-238 is then just under 3 grams. The inhalation and
ingestion limits for radioactive substances are usually given in
microcuries.
A related unit, the rutherford (rd) was also proposed
1 rd = 1,000,000 disintegrations/sec
but does not seem to be widely used. One has
1 Ci = 3.7 E4 rd exactly, and
1 rd = 27.027 microCi, approx
Another unit, the becquerel (bq) is
1 bq = 1 disintegration/sec; one has
1 Ci = 3.7 E10 bq exactly
1 bq = 2.7027 E-11 Ci (27.027 pCi) approx
As small a unit as the becquerel is, this writer has seen even the
millibecquerel (mbq), about 2.7 E-14 Ci or 0.027 pCi, used as a unit!
Several units of radioactivity from the standpoint of radiation exposure
or "dose" are extant. These consider the amount of energy being ABSORBED,
as opposed to what is emitted by a source. The first such unit established
(in 1937) was the roentgen (named for Wilhelm Roentgen, who discovered
X-rays in 1895, for which he won the very first (1901) Nobel Prize in
Physics). The roentgen (1 r) is defined as the amount of X- or gamma
radiation that will produce 1 electrostatic unit of electricity [2.08 E9
ion pairs] in 1 cc of dry air at STP. This corresponds to the absorption by
1g of air of about 86 ergs of energy.
It was proposed to define the "rep" (roentgen equivalent physical) as the
amount of radiation (alpha and beta particles included), which upon
absorption, releases 86 ergs per gram of soft tissue (to correspond to the
roentgen). However, uncertainty about ionization energy, and even more the
difference in absorption between soft tissue and bone, rendered the rep
unsatisfactory.
The next unit actually adopted was the rad, 1 rad being defined as the
amount of radiation which releases 100 ergs per gram of absorbing material.
An acute whole-body exposure of about 600 rads is generally fatal.
The unit most commonly used today is the "roentgen equivalent man" or rem,
or the associated millirem, 1/1000 of a rem. One rem was defined as the
amount of radiation producing the same biological damage as 1 rep of X- or
gamma rays. This was changed by defining the "relative biological
effectiveness" (RBE) for particular types of radiation (relative to X- or
gamma rays), and for each type defining
dose in rems = dose in rads x RBE.
The RBE is 1 for X- and gamma rays, and for beta particles also. But the
RBE is from 10 to 20 for alpha particles, 4-5 for slow neutrons, and 10 for
fast neutrons.
It should be mentioned that alpha particles are only a radiation hazard if
emitted *inside* the body, since externally emitted alpha particles can only
penetrate a few centimeters of air, and will be stopped by the outer layer
of human skin.
Various elaborations of the rad, the rem etc have been devised to account
for localized exposure vs whole-body exposure; chronic vs acute or internal
vs external sources, etc. Unfortunately, these elaborations can lead to
confusion about the various fine distinctions being made, and advocates have
been known to use this confusion to make grossly misleading statements about
the hazards involved.
Jonathan E. Hardis
<kfo...@rmi.net> wrote:
> All right, already! If you want a conversion factor, you might be able
> to find it here. If not, you might be able to find it in one of the
> references mentioned.
You mention some good secondary sources, but not the primary ones.
Please see SP 811 and SP 330, which you can download from:
<http://physics.nist.gov/cuu/Units/bibliography.html>
For fundemental constants, see:
<http://physics.nist.gov/cuu/Constants/index.html>
> In computer-related reference, sometimes "kilo-" or "K" is used to denote
> multiplication by 1024 or 2^10; while "mega" or "M" is used for 1,048,576 or
> 2^20, and "giga" or "G" is used for 1,073,741,824 or 2^30.
In SI, "k" (not "K") is always 1000, never 1024. Similarly for "M" and "G".
However, the IEC has adopted a new convention which is catching on:
kibi (kb) is 2^10 (1024), Mebi (Mb) is 2^20, and Gibi (Gb) is 2^30.
> 1 statute mile (mi) = 5280 ft = 1760 yd = 1.609344 km
By the way, the "mile" used by the U.S. Geological survey is different.
It's the pre-1959 mile. (Parts in 10^6 differences become significant
when you're measuring something big, like Montana.)
> Strictly speaking, a weight is a force
Strictly speaking, "weight" is ambiguous. In physics textbooks, it almost
always means a force. In the supermarket and hardware store, it almost
always means mass. (And merchants have been using the term a lot longer
than physicists have.)
You accept as much, latter in your message:
> AVOIRDUPOIS WEIGHT
>
> 1 grain (gr) = 64.79891 mg = 6.479891 E-5 kg exactly
See!
> Fortunately, there is no real harm in expressing "weights" in mass units,
> PROVIDED this is understood to mean "has the same weight as". Thus, to say
> something "weighs" 1 kilogram is technically incorrect, but, if understood
> to mean "has the same weight as a kilogram mass", it would not only be
> acceptable, but would remain true independent of location!
Simpler version: there's no harm in expressing "weights" in mass units if
you are refering to masses. If you are refering to forces, use force
units.
> The "pounds" used in weighing are below taken as masses. The pound
> Avoirdupois is defined as a mass, in terms of the kilogram.
Bingo!
- Jonathan